一元高次方程C语言实现(最高五次)

1、元高次方程c语言实现(windows VC6.O本)注意：如果在linux vine或者UNIX以及非windows的系统下运行的话将代码pow以及 sqrt全部替换为powf和sqrtf以下为代码#include <stdio . h>#include <stdlib . h>#include <math. h>#include <string . h>#define MAX 1000/* 最大递归次数为 1000次*/#define ERROR"math errorn" /* 显示错误信息*/char Fun310,fx5

2、10="" ; /* 美化输出结果*/float a1,b1,c1,d1,e1,f1;/* 宏定义高次方程各项系数最大五次*/int NUMjdg; /* 判断函数最高次数*/float FC( float a, float b); /* 解一元一次方程*/floatFC3( floata, floatb, floatc, float d); /* 解一元三次方程*/floatFC2( floata, floatb, floatc, int num); /* 解一元二次方程*/float FC4( float a, float b, float c, float d, fl

3、oat e); /* 解一元四次方程*/float FC5(); /* 解一元五次方程*/float fun( float x); /* 五次函数代值求解*/float dfun( float x); /* 五次导函数代值求解*/float iterate( float x); /* 牛顿迭代法猜值求解*/int main()float x5; /* 五次方程最后一个解*/FILE *fp; /* 解的内容以文件的形式保存*/char save;char buf256; /* 从文件内读取内容保存至buf*/buf0 ='0' ; /* 防止乱码，开头定义为 NULL*/ fp

4、 =fopen( "fun.dat" , "w");strcpy(Fun3, "" );fclose(fp);printf( "Do you want to save the result? 'y' or 'n'"); /* 是否想保存结果数据？ */printf("n->" );scanf( "%c", &save);redo:printf( "please input degree numbern->"

5、;); /* 请输入最高次数*/scanf( "%d", &NUMjdg);if (NUMjdg<1| NUMjdg>5) goto redo;printf( "the number of a?->"); /* 输入最高次项系数*/ scanf( "%f" , &a1);if (a1 =0) printf(ERROR); return 1; printf("the number of b?->"); /* 输入第二高次项系数*/scanf( "%f", &

6、amp;b1);if (NUMjdg=1) printf( "the result is %gn",FC(a1,b1); goto end1; printf("the number of c?->"); /* 输入第三高次项系数*/ scanf( "%f", &c1);if (NUMjdg=2) FC2(a1,b1,c1,1); goto end2; printf( "the number of d?->"); /* 输入第四高次项系数*/scanf( "%f" , &

7、;d1);if (NUMjdg=3) FC3(a1,b1,c1,d1); goto end3; printf( "the number of e?->"); /* 输入第五高次项系数*/scanf( "%f", &e1);if (NUMjdg=4) FC4(a1,b1,c1,d1,e1); goto end4; printf( "the number of f?->"); /* 输入常数项系数*/scanf( "%f", &f1);x5 =FC5(););end2:end4:if (a1

8、 != 0) printf( "n*nThere is following result:n fp =fopen( "fun.dat" , "r" );while (fgets(buf,256,fp) != NULL) printf( "%s",buf); fclose(fp); fp =fopen( "fun.dat" , "a" );if (NUMjdg=5) fprintf(fp, "x%s=%gn",fx5,x5);printf( "x%s=%gn

9、",fx5,x5);fclose(fp);end1:end3:if (save ='n' ) unlink( "fun.dat" ); getch();return 0;)/*以下为各项函数的定义*/float fun(float x)return(x*x*x*x*x*al+x*x*x*x*bl+x*x*x*cl+x*x*dl+x*el+fl);)float dfun(float x)return(5*al*x*x*x*x+4*bl*x*x*x+3*cl*x*x+2*dl*x+el);)float iterate(float x)float xl;

10、xl=x-fun(x)/dfun(x);return(xl);)float FC5()(int k=0, i;float x0=-2. 0, xl, de;float b, c, d, e, temp5;bl/'=al; cl/=al; dl/=al; el/=al; fl/=al; al=l. 0;printf("FC5 a=%g b=%g c=%g d=%g e=%g f=%gn，z, al, bl, cl, dl, el, fl);if (bl=二0. 0&&cl=0. 0&&dl=0. 0&&el=0. 0&&a

11、mp;fl=0. 0)(return 0. 0;temp0=-b1/5; temptl=-cl/(2*bl); temp2=-dl/cl; temp3=2*el/(-dl); temp4=-5*fl/el;for(i=0; i<5; i+) printf (，*temp%d: %gz，, i, tempi);i f (temp 0 =temp 1 &&temp 0 =temp 2 &&temp 0 =temp 3&&temp0 =temp4 )(return temp0;dok+;xl=iterate(xO);/ printf (z，%d

12、%gn”,k, xl);de=fabs(xl-xO);x0=xl;)while (de>=0.00001&&k<MAX);strcpy(fx5,"”)；b =b1+x1; c =c1+b* x1; d =d1+c*x1; e =e1+d* x1;FC4(1.0,b,c,d,e);printf( "one of the result is %gn",x1);return x1;/* 解法请参照盛金公式，费拉里公式，牛顿迭代法，一元二次求根公式 */float FC4( float a, float b, float c, float d,

13、 float e)float y;float M,N,P;float y04;int i;b /= a; c /= a; d /= a; e /= a; a =1.0;printf( "FC4 a:%g b:%g c:%g d:%g e:%gn" ,a,b,c,d,e);y00 =8.0;y01 =-4.0*c;y02 =-1*(8.0 *e-2.0*b*d);y03 =-e*(b*b-4.0*c) -d*d;for (i =1;i <=3;i +) printf( "y%d:%g",i,y0i);printf( "n" );y

14、 =FC3(y00,y01,y02,y03);printf( "y:%g " ,y);M =sqrt(8.0 *y+b*b-4.0*c);N =b*y-d;printf( "M:%g N:%gn" ,M,N);if (M=0)P =sqrt(y *y-e);printf( "P:%gn" ,P);FC2(2.0,b,2.0*(y +P),1);FC2(2.0,b,2.0*(y-P),3);elseFC2(2.0,b+M,2.0*(y+N/ M),1);FC2(2.0,b- M,2.0*(y- N/ M),3);return 0.0;

15、float FC3( float a, float b, float c, float d)float A,B,C,delta,x3,ni,fun3;float y1,y2,k,T,theta;float temp;FILE *fp;int i,y_1 =1,y_2 =1;printf("FC3->a=%g b=%g c=%g d=%gn",a,b,c,d);A =b*b-3*a*c;B =b*c-9*a*d;C =c*c-3*b*d;delta =B* B-4*A*C;printf( "fc3A:%g B:%g C:%gn" ,A,B,C);pr

16、intf( "fc3 delta:%gn" ,delta);if (NUMjdg=3) printf( "There is following result:nn" ); fp =fopen( "fun.dat" , "w");elsestrcpy(Fun3, "fun3:" );if (delta =0)if (A=B)if (b =0) printf( "%sx1=x2=x3=%dn",Fun3,0); else printf( "%sx1=x2=x3=%gn&

17、quot; ,Fun3, - b/ (3*a); if (b =0) fprintf(fp, "%sx1=x2=x3=%dn",Fun3,0); else fprintf(fp, "%sx1=x2=x3=%gn" ,Fun3, -b/ (3*a); fun0 =-b/ (3*a);fun1 =fun0;fun2 =fun1;if (NUMjdg=3) printf( "n" ); fclose(fp); return fun0; elsek =B/ A;printf("%sx1=%gn" ,Fun3,fun0 =-

18、b/ a+k);printf("%sx2=%gn" ,Fun3,fun1 =-k/2);fprintf(fp,"%sx1=%gn" ,Fun3,fun0 =-b/ a+k);fprintf(fp,"%sx2=%gn" ,Fun3,fun1 =-k/2);if (NUMjdg=3) printf( "n" ); fclose(fp); if (fun0 >fun1)return fun0;elsereturn fun1;else if (delta >0)y1 =A* b+1.5 *a*(- B+pow(

19、delta,0.5);if (y1 <0.0)y_1=-1;y2 =A* b+1.5 *a*(- B- pow(delta,0.5);if (y2 <0)y_2=-1;if (NUMjdg!= 3)printf( "y1: %gny2: %gn" ,y1,y2); x0=(- b- y_1* pow(fabs(y1),1.0 / 3.0) -y_2*pow(fabs(y2),1.0 / 3.0) / (3*a);x1=(-2*b+y_1*pow(fabs(y1),1.0 / 3.0) +y_2*pow(fabs(y2),1.0 / 3.0) / (6*a);ni

20、 =pow(3.0,0.5) * (y_1 * pow(fabs(y1),1.0 / 3.0) -y_2*pow(fabs(y2),1.0 / 3.0) / (6*a);printf("%sx1=%gn" ,Fun3,fun0 =x0);printf("%sx2=%g+%gin" ,Fun3,x1,fabs(ni);printf("%sx3=%g-%gin" ,Fun3,x1,fabs(ni);fprintf(fp,"%sx1=%gn" ,Fun3,fun0 =x0);fprintf(fp,"%sx2=%

21、g+%gin" ,Fun3,x1,fabs(ni);fprintf(fp,"%sx3=%g-%gin" ,Fun3,x1,fabs(ni);fun1=fun0;fun2=fun1;if (NUMjdg=3) printf( "n" ); fclose(fp); return fun0;elseT =(2*A*b-3*a*B)/(2*pow(A,1.5);theta=acos( T);theta/= 3;if (NUMjdg!= 3) printf("T:%gn" ,T);printf("theta: %gn&quo

22、t; ,theta); /cs = theta+2/3*i*acos(-1);x0=(- b-2*pow(A,0.5) * cos(theta) / (3*a);x1=(- b+pow(A,0.5) *(cos(theta) +pow(3,0.5) *sin(theta)/ (3*a);x2=(- b+pow(A,0.5) *(cos(theta) - pow(3,0.5) *sin(theta)/ (3*a);for (i =0;i <3;i +) printf( "%sx%d=%gn",Fun3,i +1,funi =xi);if (NUMjdg=3)for (i =0;i <3;i +) fprintf(fp, "%sx%d=%gn",Fun3,i +1,funi =xi); if (fun0 >fun1) temp=fun0; else temp=fun1; if (NUMjdg=3) printf( "n" ); fclose(fp); if (temp>fun2)return temp; elsereturn fun2; float FC2( float a,